Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-5x-7y &= 1 \\ 5x+9y &= 3\end{align*}$
Solution: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $2y = 4$ Divide both sides by $2$ and reduce as necessary. $y = 2$ Substitute $2$ for $y$ in the top equation. $-5x-7( 2) = 1$ $-5x-14 = 1$ $-5x = 15$ $x = -3$ The solution is $\enspace x = -3, \enspace y = 2$.